9n+3n^2=176.75

Simple and best practice solution for 9n+3n^2=176.75 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 9n+3n^2=176.75 equation:


Simplifying
9n + 3n2 = 176.75

Solving
9n + 3n2 = 176.75

Solving for variable 'n'.

Reorder the terms:
-176.75 + 9n + 3n2 = 176.75 + -176.75

Combine like terms: 176.75 + -176.75 = 0.00
-176.75 + 9n + 3n2 = 0.00

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-58.91666667 + 3n + n2 = 0.00

Move the constant term to the right:

Add '58.91666667' to each side of the equation.
-58.91666667 + 3n + 58.91666667 + n2 = 0.00 + 58.91666667

Reorder the terms:
-58.91666667 + 58.91666667 + 3n + n2 = 0.00 + 58.91666667

Combine like terms: -58.91666667 + 58.91666667 = 0.00000000
0.00000000 + 3n + n2 = 0.00 + 58.91666667
3n + n2 = 0.00 + 58.91666667

Combine like terms: 0.00 + 58.91666667 = 58.91666667
3n + n2 = 58.91666667

The n term is 3n.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3n + 2.25 + n2 = 58.91666667 + 2.25

Reorder the terms:
2.25 + 3n + n2 = 58.91666667 + 2.25

Combine like terms: 58.91666667 + 2.25 = 61.16666667
2.25 + 3n + n2 = 61.16666667

Factor a perfect square on the left side:
(n + 1.5)(n + 1.5) = 61.16666667

Calculate the square root of the right side: 7.820912138

Break this problem into two subproblems by setting 
(n + 1.5) equal to 7.820912138 and -7.820912138.

Subproblem 1

n + 1.5 = 7.820912138 Simplifying n + 1.5 = 7.820912138 Reorder the terms: 1.5 + n = 7.820912138 Solving 1.5 + n = 7.820912138 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + n = 7.820912138 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = 7.820912138 + -1.5 n = 7.820912138 + -1.5 Combine like terms: 7.820912138 + -1.5 = 6.320912138 n = 6.320912138 Simplifying n = 6.320912138

Subproblem 2

n + 1.5 = -7.820912138 Simplifying n + 1.5 = -7.820912138 Reorder the terms: 1.5 + n = -7.820912138 Solving 1.5 + n = -7.820912138 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + n = -7.820912138 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + n = -7.820912138 + -1.5 n = -7.820912138 + -1.5 Combine like terms: -7.820912138 + -1.5 = -9.320912138 n = -9.320912138 Simplifying n = -9.320912138

Solution

The solution to the problem is based on the solutions from the subproblems. n = {6.320912138, -9.320912138}

See similar equations:

| x^4-7x^2+16=0 | | 3p+6=6-p | | 16(v+1)-4v=4(3v+1)-7 | | M+2m+-6=-12+2m | | y^2dx+(3xy+y^2-1)dy=0 | | A=5n-600 | | y=.5x-10 | | 4z+z+5=z | | -19=x+3(2x-4) | | -3x+15=2x-2 | | 31=s+2.5s+10 | | 10x^2-5=0 | | 2(12-4y)+4y=24 | | 7g-21=16 | | sqrt(x+21)-1=x | | 5f-3=32 | | 183=-w+87 | | X-26=12 | | 25m^2a^2-4a^2= | | 3(12)+y=36 | | 4.7m=18-2.7m | | 12k+50=40 | | 49x-16x^3=0 | | -2=(7y-8y)2+14 | | (9n+4)+(3n^2-0.75)=180 | | -5h-13=-28 | | x^2-70=7x | | -x+5=2(x-8) | | 10x-6=3x-5 | | W-26=12 | | 9x+6y=n | | N+3=15-6 |

Equations solver categories